

A099308


Numbers n whose kth arithmetic derivative is zero for some k. Complement of A099309.


16



0, 1, 2, 3, 5, 6, 7, 9, 10, 11, 13, 14, 17, 18, 19, 21, 22, 23, 25, 29, 30, 31, 33, 34, 37, 38, 41, 42, 43, 46, 47, 49, 53, 57, 58, 59, 61, 62, 65, 66, 67, 70, 71, 73, 77, 78, 79, 82, 83, 85, 89, 93, 94, 97, 98, 101, 103, 105, 107, 109, 113, 114, 118, 121, 126, 127, 129, 130
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OFFSET

1,3


COMMENTS

The first derivative of 0 and 1 is 0. The second derivative of a prime number is 0.


REFERENCES

See A003415


LINKS

T. D. Noe, Table of n, a(n) for n = 1..10000


EXAMPLE

18 is on this list because the first through fifth derivatives are 21, 10, 7, 1, 0


MATHEMATICA

dn[0]=0; dn[1]=0; dn[n_]:=Module[{f=Transpose[FactorInteger[n]]}, If[PrimeQ[n], 1, Plus@@(n*f[[2]]/f[[1]])]]; d1=Table[dn[n], {n, 40000}]; nLim=200; lst={1}; i=1; While[i<=Length[lst], currN=lst[[i]]; pre=Intersection[Flatten[Position[d1, currN]], Range[nLim]]; pre=Complement[pre, lst]; lst=Join[lst, pre]; i++ ]; Union[lst]


CROSSREFS

Cf. A003415 (arithmetic derivative of n), A099307 (least k such that the kth arithmetic derivative of n is zero), A099309 (numbers whose kth arithmetic derivative is nonzero for all k).
Sequence in context: A305847 A248565 A065896 * A074235 A325366 A192189
Adjacent sequences: A099305 A099306 A099307 * A099309 A099310 A099311


KEYWORD

nonn


AUTHOR

T. D. Noe, Oct 12 2004


STATUS

approved



